Elastic/Plastic Discs Under Plane Stress Conditions (eBook)

Sergey Alexandrov (Autor)

eBook Download: PDF

2015 | 2015
XI, 113 Seiten
Springer International Publishing (Verlag)
978-3-319-14580-8 (ISBN)

Infos

This Volume presents a unified approach to calculate the plane stress distribution of stress and strain in thin elastic/plastic discs subject to various loading conditions. There is a vast amount of literature on analytical and semi-analytical solutions for such discs obeying Tresca's yield criterion and its associated flow rule. On the other hand, most of analytical and semi-analytical solutions for Mises yield criterion are based on the deformation theory of plasticity. A distinguished feature of the solutions given in the present volume is that the flow theory of plasticity and Mises yield criterion are adopted. The solutions are semi-analytical in the sense that numerical methods are only necessary to evaluate ordinary integrals and solve transcendental equations. The book shows that under certain conditions solutions based on the deformation and flow theories of plasticity coincide. All the solutions are illustrated with numerical examples. The goal of the book is to provide the reader with a vision and an insight into the problems of analysis and design of elastic/plastic discs. The limitations and the applicability of solutions are emphasized. The book is written for engineers, graduate students and researchers interested in the development of techniques for analysis and design of thin elastic/plastic discs.

Inhalt

Preface 6
Acknowledgments 8
Contents 9
Symbols 11
1 Axisymmetric Thermo-Elastic-Plastic Problem Under Plane Stress Conditions 12
1.1 Introduction 12
1.2 Basic Equations 13
1.3 General Stress Solutions 19
1.3.1 General Thermo/Elastic Solution 19
1.3.2 Yield Criterion (1.5) 19
1.3.3 Yield Criterion (1.8) 20
1.3.4 Yield Criterion (1.11) 22
1.4 General Strain Solutions 24
1.4.1 General Thermo/Elastic Solution 24
1.4.2 Yield Criterion (1.5) 25
1.4.3 Yield Criterion (1.8) 28
1.4.4 Yield Criterion (1.11) 30
References 34
2 Mechanical Loading 37
2.1 Disc Under Internal Pressure 37
2.1.1 Yield Criterion (1.51.5) 38
2.1.2 Yield Criterion (1.81.8) 43
2.1.3 Yield Criterion (1.111.11) 60
2.2 Disc Under External Pressure 73
2.2.1 Yield Criterion (1.51.5) 80
2.2.2 Yield Criterion (1.81.8) 84
2.2.3 Yield Criterion (1.111.11) 95
References 100
3 Thermal Loading 102
3.1 Disc Loaded by Uniform Temperature Field 102
3.1.1 Yield Criterion (1.51.5) 103
3.1.2 Yield Criterion (1.81.8) 107
3.1.3 Yield Criterion (1.111.11) 117

Produkt-Details

• Erscheint lt. Verlag: 15.4.2015
• Reihe/Serie: SpringerBriefs in Applied Sciences and Technology
• Reihe/Serie: SpringerBriefs in Computational Mechanics
• Zusatzinfo: XI, 113 p. 44 illus.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Analytic Solutions • failure mechanisms • flow theory • Limit State • Mises Yield Criterion • Tresca Yield Criterion • Unified Approach
• ISBN-10: 3-319-14580-0 / 3319145800
• ISBN-13: 978-3-319-14580-8 / 9783319145808